Selforganisational High Efﬁcient Stable Chaos Patterns

Bernhard Heiden

1,3 a

, Volodymyr Alieksieiev

2 b

and Bianca Tonino-Heiden

3 c

1

Industrial Engineering and Management Studiengang, University of Applied Sciences, Europastrasse 4, Villach, Austria

2

Faculty of Mechanical Engineering, Leibniz University Hannover, An der Universit

¨

at 1, Garbsen, Germany

3

Philosophy Institute, University of Graz, Heinrichstraße 26/V, Graz, Austria

Keywords:

Logistics, Witness, Mathcad, Multirobots, Selforganisation, Educational Tool, Chaos Theory, IoT

Application, Information Entropy, Stable Chaos.

Abstract:

The aim of this paper is to provide a new solution for the problem of a simple application of swarm robots, and

here the model and its simulation, which shall be later implemented in these Internet of Things (IoT) devices.

For this reason this paper describes how, swarm robots, robot-multirobots, a series of entangled robots or robot-

os, form predictable selforganisational room-time patterns, as a function of a binary sensor and a binary actor

signal interaction, in a triangular cellular automata fashion. The inﬂuence of the outer border compared to the

inner border of robot-os is investigated, to answer the question, whether and how they can be distinguished.

So this process can then be regarded as a different level border-order-entity or as a ’solidiﬁcation process’

of the robot-o. By means of this, the robot-o is itself ’recognising’, as an extended self, that is identiﬁed

by the robot-o as the environment. Border as direction change of signal, hence, can be regarded as a basic

selforganisational driving force. Above described sensor actor processes can be regarded as bidirectional

ordering process, according to orgiton theory, a further development of the theory of selforganisation. Based

on the Shannon information entropy, measuring this is methodically demonstrated. Application programs and

respective patterns are given in Mathcad and Witness simulations in detail. These prepare for IoT robot-os

applications, for future research applications, especially for the open source robot-os of Elmenreich et al., that

our work refers to and builds upon.

1 INTRODUCTION

Selforganisational patterns are quite well known, but

it seems, that these become more and more relevant in

technical and cyber-physical applications like Inter-

net of Things (IoT)-devices. There are several reasons

for this. Cybernetic models have become increasingly

complex in the sense of programming on the one side,

on the other side there is the need for efﬁcient designs

of programming in limited resources regions applica-

tions, e.g. in space missions, autonomous vehicles, or

transport-tools, and others. The limited resources are

not only part of some exotic and maybe extreme ap-

plications, but they arise also increasingly in common

applications like production environments. One rea-

son is, that the extreme situation can be understood

as solving an optimality problem of e.g. maximum

production while at the same time a lot of restric-

a

https://orcid.org/0000-0001-8324-6505

b

https://orcid.org/0000-0003-0792-3740

c

https://orcid.org/0000-0001-7648-2833

tions or system-environment conditions have to be

fulﬁlled. In this ﬁeld of increasingly complex condi-

tions, not only not all information is available timely,

but also some information is impossible reachable or

in out of distance conditions. We all know now, as in

the current pandemic video-conferencing is becoming

widely common, the acquainted systemic problem is,

that reliant information of the ’end-point’, becomes

increasingly important, which means that the problem

has to be solved to operate safely in industrial produc-

tion, etc. out of a distant operating point.

While this may be clear for military applications,

the civilian applications are now also affected system-

ically.

We can think of this, as increasing growth of inter-

mediate relay stations between information transmit-

ter and receiver used in the path between IoT-devices.

This has been recently named by the term osmotic

manufacturing (Heiden et al., 2020), osmotic comput-

ing (Villari et al., 2016), and also as a generalisation

the osmotic paradigm. (Heiden et al., 2021a; Heiden

et al., 2021b).

Heiden, B., Alieksieiev, V. and Tonino-Heiden, B.

Selforganisational High Efﬁcient Stable Chaos Patterns.

DOI: 10.5220/0010465502450252

In Proceedings of the 6th International Conference on Internet of Things, Big Data and Security (IoTBDS 2021), pages 245-252

ISBN: 978-989-758-504-3

Copyright

c

2021 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

245

As such the complexity measure of IoT-systems

becomes increasingly important. One such measure

is the Lyapunov coefﬁcient, another the information

entropy by Shannon (Shannon and Weaver, 1963). In

this work, this measure will be used to order the in-

formation results obtained in the calculation.

The inspiration of this work is that chaotic pat-

terns can be implemented by algorithms looking just

at neighbors, which result in e.g. Sierpinski triangle

patterns (H

¨

utt, 2006).

This has lead to the idea of this work to implement

the pattern generators on IoT devices of swarm type.

That means each IoT device is similar and can imple-

ment cybernetics. One such system can then be re-

garded as a multirobots (Elmenreich et al., 2015) im-

plementation. Synonyms are robots, swarm robots or

robot-os. Robot-o refers to the term robot-orgiton, ac-

cording to the grammar rules of orgiton theory (Hei-

den and Tonino-Heiden, 2021). An orgiton is a cyber-

netic unit with elements of mass, energy and infor-

mation, and hence the robot-o denotes a single robot,

as well as a swarm, which is then a robot-o of poten-

tially higher order. On each ”length” scale a robot-o

denotes a functional unit with a speciﬁc composition.

As a consequence, the system can be used to study

chaotic patterns with robot-os or IoT-clusters in gen-

eral.

1.1 Content

This work is, after summarising the goal in section

1.2 with the basic idea of this work of tri-information

patterns, diving in section 2, into the related theoret-

ical background. In section 3 we go to the computa-

tional applications of tri-information-patterns, ﬁrst in

section 3.1 to a Mathcad application, then in section

3.2 to a Witness application, and we close section 3

with an information entropy investigation in section

3.3. In section 4 we make conclusions of the compu-

tational applications and connect them to IoT appli-

cations. Finally, we give a summary and outlook in

section 5.

1.2 Goal

The goal of this work, is to motivate and give appli-

cation examples of chaotic patterns in computational

and IoT devices, designated for educational purposes,

leading to a deeper understanding of chaotic system

behaviour of cellular automata, implemented in paral-

lelised IoT-swarms, operating in stable chaos regions.

For this basic computational tools for IoT-swarm ap-

plications in general, and educational ones in special

are given.

2 TRI-INFORMATION PATTERNS

In this section we will introduce a concept used in this

paper and based on the following:

Axiom 1. Information ﬂow is a translational infor-

mation chain. - The ”living” function can be inter-

preted as a continuous information ﬂow.

We here regard cybernetic systems, analogously to

Wiener (Wiener, 1963), similar to living ”machines”,

or as Heinz von F

¨

orster noted, biocybernetic ma-

chines.

Axiom 2. Increasingly nested translational patterns

(autoencoders), increase potentially order and allow

for increasingly safety or an integrity informational

check.

When Axiom 2 is true, then this should also be

seen in some informational measure. Such a measure

could be the informational entropy S

i

. The Shannon

information entropy S

i

can be calculated by (1):

H

i

= S

i

= p

i

· ln(p

i

) (1)

p

i

denotes here the probability or frequency. This

measure can be in general used to measure informa-

tion content, as a consequence of its statistical prop-

erties. We will use this when looking at some bit-

information of the core translation process of the cel-

lular automata. The translation process can be re-

garded as an essential process transferring informa-

tion from one moment to the other (event horizon) or

one room to the other (cf. Figure 1). By this means,

information of one observing window in Figure 1 is

divided by ’mirroring’ borders and fulﬁlling, in each

window, the information balance. By this dynami-

cally information can be kept alive in an open system,

as well as be enriched by open time-rooms or room-

times of possibility.

3 SIMULATION

In the following, we give the two simulation-

programs for the tri-information chaos patterns of

the cellular automata. The translational matrix is U

(see APPENDIX - MATHCAD PROGRAMS). Eight

combinatorial possible states of three elements, or

one element and its two neighbours, are combined

uniquely by one translational conﬁguration, which is

in our case row four in U.

The ﬁrst simulation is done in Mathcad. A paral-

lelised program for general process simulation is Wit-

ness. This has the advantage to be able to simulate

each virtual IoT device, which is operating in the IoT-

swarm, separately. We show, how this is implemented

in this speciﬁc ”parallel” program environment.

IoTBDS 2021 - 6th International Conference on Internet of Things, Big Data and Security

246

information

translation

previous state

information

later state

information

metainformation

information

information

Room Mirror

from inner to outer

actual event location of observer

single to multi

Time Mirror

from earlier to later

actual event horizon of observer

serial to multiparallel

+1

+1+1

+1

+1

information

metainformation

meta-

metainformation

+1

+1

+1

+1

indication of emergence - a new observer reality

-1

indication of disemergence - a past observer reality

-1

-1

-1

-1

-1

-1

-1

mirror axes / planes

x

y

Figure 1: Room-time information multiplication dimension connectivity.

The programs, in Mathcad or Witness itself, can be re-

garded as information-translation in the sense of Fig-

ure 1, and hence the system order is increasing poten-

tially.

3.1 Mathcad Simulation

To simulate the triangular process ﬁrst two programs

are made in Mathcad (cf. APPENDIX - MATHCAD

PROGRAMS) to implement the cellular automaton.

In Figure 2 we see the cyclic implementation. Cir-

cular robot-os, can be imagined in a way having one

neighbour to the left and one to the right and arranged

in a circle.

The other variant is to have robot-os with left and

right neighbours only, which means that there is an

open-end on each side (cf. Figure 3).

In Figure 4 ten (10) variants of open-ended and

cycle robot-os patterns can be seen. They tend to a

stable dynamic pattern, although, each conﬁguration

is more or less chaotic in the pattern structure, or has

different information entropy (cf. Figure 6).

3.2 Witness Simulation

Nowadays the role of Machine-to-Machine (M2M)

communication is becoming increasingly important

in different areas of applications. M2M communi-

cation technology is commonly based on wired or

wireless communication channels, e.g. sensors, In-

ternet, RFID, etc. (Galeti

´

c et al., 2011). The pur-

pose of this chapter is to introduce a simple simula-

Figure 2: With the A3xc(n=5,m=15) function (see AP-

PENDIX - MATHCAD PROGRAMS) calculated cyclic

pattern of ﬁve robot-os for 15 time steps (n=5, m=15); left

the pattern-picture and right the corresponding 0/1 repre-

sentational matrix.

tion model as a pattern example of communication be-

tween functional independent and informational open

robots-multirobots as an entangled robotic system.

The model was simulated in the Witness Software

and consists of ﬁve functional independent robots,

each of which has binary incoming and outgoing sig-

nals. The functional principle of communication in

this robotic system is based on binary sensor and bi-

Selforganisational High Efﬁcient Stable Chaos Patterns

247

Figure 3: With the A3x(n=5,m=15) function (see AP-

PENDIX - MATHCAD PROGRAMS) calculated cyclic

pattern of ﬁve robot-os for 15 time steps (n=5, m=15); left

the pattern-picture and right the corresponding 0/1 repre-

sentational matrix - open-ended variant.

nary actor signals. Each robot recognises and pro-

cesses signals of its neighbouring robots (input sig-

nal) according to the general pattern and generates

the outgoing signals (output). For a demonstration of

outgoing signals, the function of integer variables in

Witness was used. Based on this simulation, the inner

and external border of a robot-o can be distinguished

This methodology of M2M-communication-based on

binary sensors can be also important and applicable

in intralogistics, namely in the context of trafﬁc or-

ganisation of automated guided vehicles and human-

robot-communication in the intelligent warehouse (cf.

(Rey et al., 2019)).

When we look at the Witness simulation, there is

the basic concept of parallelisation of the model. Wit-

ness is an intrinsic simultaneous process simulation

program. By this, each robot can be regarded as a par-

allel and individual separate agent in one room-time

window, according to Figure 1. The parallelisation

process occurs then by going into the y-direction. An

example conﬁguration of the ﬁve robot-os is depicted

in Figure 5. In the Witness model, the information

balance of the ’living’ or dynamic cybernetic process

is given by ingoing and outgoing information. In this

context, the ingoing part and outgoing part of every

robot-o simulates the event horizon for each time step.

In this event horizon then the translation to the next

step is calculated inside the robot (cf. Figure 5, 1 and

APPENDIX - WITNESS PROGRAMS). The transla-

tion is done in this case according to the cellular au-

tomaton and is by this restricted to a relatively static

as well as collective behaviour between each state, so

this may be called a swarm.

When we now regard a meta-meta perspective, an

observer who sees the light of the robot-os, this ob-

server gets integrated information of all together as

a pattern. This meta-information then increases the

possibilities of the process, and hence the possible

practical applications.

3.3 Information Entropy

In Figure 6 the information entropy according to

Shannon and equation (1) is calculated for the 2 x 10

variants in Figure 4, as well as the intermediate steps.

The general form in Mathcad can be written:

H(n) := log(n, 2) (2)

So we have calculated the maximum possible entropy

(Hmax = H(n ∗ m) according to (2)), the entropy for

the cycle cases (H cyclic= number of positive values

in A33x (see function summe1(n, m) in APPENDIX -

MATHCAD PROGRAMS)), the entropy of the open-

end cases (H open end), and the difference entropy

for cyclic (DeltaH cyclic) and for the open-end cases

(DeltaH open end) and the maximum time horizon

(regarded time steps). The total bit number is then

time steps x # robot-os (number (n) of robot-os). We

see then peaks in n=3,5,9,17 which correspond to in-

creasing relative entropy in those cases as the signal is

vanishing after a certain time, for the depicted open-

end cases (cf. Figure 4).

We can ﬁnd also the minimum entropy differ-

ences, and hence the maximum efﬁciency patterns for

n=3 robots for the cyclic cases and n=7 for the open-

end cases, where the information efﬁciency is maxi-

mal in the cyclic n=3 cases.

When the difference is minimal with regard to

maximum entropy, information is most effectively

stored in the patterns. This is the case at the local

minima of DeltaH in Figure 6.

Of course, this is only valid for the given time-

horizon and the translational vector in row 4 given in

U. In sum, in this scenario 2

8

= 256 cases are possi-

ble.

4 CONCLUSION

We can conclude from the above given computational

results, that it is possible to implement a stable chaotic

pattern by means of cellular automata and different

forms of translations. Translations are understood

as a program inside of an observer. When progress-

ing with information from inside to outside and or in

IoTBDS 2021 - 6th International Conference on Internet of Things, Big Data and Security

248

Figure 4: Ten (10) variants with the open-ended and the cyclic robot-os implementation.

Figure 5: Triangularity pattern simulation in Witness with

ﬁve robot-os.

time, then the possibilities can emerge by the grade of

increasing possibilities triggered by the speciﬁc pro-

cess. By this, the difference lies in the expression of

how information is distributed, e.g. with regard to in-

formation entropy.

This then lets order or control the process from

extended mirroring planes by means of observables

that constitute a dynamic memory. In each case, in

these cellular automata, the information balance can

be regarded as fulﬁlled for each event window, i.e. it

constitutes a living system, only having possibilities

in the ’alive’ state, which means that information is

in- and outgoing with regard to the observer.

More speciﬁcally the observer constitutes an

event-horizon decreasing effect of possibilities by ob-

servation. The same is true for acting.

Figure 6: Information entropy.

Hence in the robot-o case, the basic constitution

of a cellular automaton - which can therefore also be

regarded as the most efﬁcient with regard to cause-

effect, as it maximises the possibilities room - is a dy-

namic cybernetic interaction, including sensing and

acting. This in sum is the form of the translation pro-

cess, of an observer/actor reality autoencoder, which

means that ingoing and outgoing information with re-

gard to a process or event relative observer is in dy-

namic equilibrium.

The emergence process is here different. It arises

in each room-time window as a consequence of the

possibilities rooms and is hence related to entropy

resp. negentropy.

Hence stable chaos is bound to this basic infor-

mation and more complex patterns are triggered for

the same translation procedure, if there are employed

more observers or e.g. robot-os.

Selforganisational High Efﬁcient Stable Chaos Patterns

249

An interesting fact is that the same overall pro-

gram, which explicitly excludes different patterns in

individual robot-os, restricts information order, which

can be derived from Figure 6. This is as a sum a

unidirectional process, which can be regarded as ’so-

lidiﬁed’ in a state, the translation vector. As a con-

clusion, the bidirectionality would possibly increase

order (cf. (Heiden and Tonino-Heiden, 2021)). The

gaining possibilities are then restricted to the differ-

ence to the unidirectional case, as a consequence. A

future research could then be to investigate, how the

bidirectional process is achieved and what the infor-

mational efﬁciency gain will be.

As a conclusion with regard to information en-

tropy it can be said, that this is dependent on the room-

time horizon, and there exists a minimum leading to a

stable efﬁcient chaotic pattern. Similar results are to

be expected with other translational patterns and can

be measured with the given method.

In general, the ”efﬁciency” case, will be also a

question of the speciﬁc application, and hence it will

change, according to different patterns. It may then be

optimal with regard to a speciﬁc informational goal,

e.g. detection of an error intrusion, detection of sta-

ble operation, signal encryption, signal superposition,

dynamic signal storage, etc.

5 SUMMARY AND OUTLOOK

In this work, we have given the computational tools

to implement stable chaotic patterns by means of cel-

lular automata. The basic principles have been pro-

vided, that can be applied in future research to IoT-

swarm applications like in robot-os.

Future applications in IoT-swarms will have to im-

plement further ”translations” into physical devices

according to the theory section 2.

There can be used similar programs as in the Wit-

ness program section, with the difference, that the

program, e.g. on the Arduino-Board has to be con-

nected to the input (light-sensing) and output (light-

indicating) information resp. signal.

Concerning the translation matrix only one of 256

possibilities, according to permutations has been in-

vestigated. So using other translational codes, a lot of

more conﬁgurations are possible. It will be interest-

ing, maybe for future research, to investigate the re-

lation of those different kinds of translational patterns

on the overall informational process, as well as more

dynamic or even more nested translations relation-

matrices, maybe to implement bi-directional cyber-

netic processes to further increase the informational

efﬁciency of the regarded or implemented processes.

REFERENCES

Elmenreich, W., Heiden, B., Reiner, G., and Zhevzhyk, S.

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c, V., Boji

´

c, I., Ku

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sek, M., Je

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zi

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c, G., De

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si

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c, S., and

Huljeni

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c, D. (2011). Basic principles of machine-to-

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utzt sie zum Naturverst

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andnis?, pages 91–105.

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IoTBDS 2021 - 6th International Conference on Internet of Things, Big Data and Security

250

APPENDIX

Mathcad Programs

Translational Matrix U:

Starting Vector:

Initial Matrix:

Mathcad Program A33x(n, m) - non-cyclic (open-

ended) triangular cellular automaton (nxm, n...robots,

m...time steps):

Mathcad Program A33xc(n, m) - cyclic triangular cel-

lular automaton (nxm, n...robots, m...time steps):

summe1(n, m) - for the calculation of entropy in the

open-end case:

summe1c(n, m) - for the calculation of entropy in the

cyclic case:

Calculation of entropy:

Witness Programs

Actions Initialise

R1L = 0

R2L = 0

R3L = 0

R4L = 0

R5L = 0

R1La = 0

R2La = 0

R3La = 1

R4La = 0

R5La = 0

X1 = 0

X2 = 0

X3 = 0

X4 = 0

X5 = 0

r1t = 0

r2t = 0

r3t = 0

r4t = 0

Selforganisational High Efﬁcient Stable Chaos Patterns

251

r5t = 0

timeo = 0

timen = 0

tt = 1

Robot1-Program-Actions: Input Part

IF R5La = 1 AND R1La = 1 AND R2La = 1

X1 = 0

r1t = 1

ELSEIF R5La = 1 AND R1La = 1 AND R2La = 0

X1 = 1

r1t = 2

ELSEIF R5La = 1 AND R1La = 0 AND R2La = 1

X1 = 0

r1t = 3

ELSEIF R5La = 1 AND R1La = 0 AND R2La = 0

X1 = 1

r1t = 4

ELSEIF R5La = 0 AND R1La = 1 AND R2La = 1

X1 = 1

r1t = 5

ELSEIF R5La = 0 AND R1La = 1 AND R2La = 0

X1 = 0

r1t = 6

ELSEIF R5La = 0 AND R1La = 0 AND R2La = 1

X1 = 1

r1t = 7

ELSEIF R5La = 0 AND R1La = 0 AND R2La = 0

X1 = 0

r1t = 8

ENDIF

R1L = X1

timex = TIME

IF TIME > timeo

timen = TIME

timeo = timen - 1

ENDIF

Robot1-Program-Actions: Output Part

IF TIME = 1

XLWriteArray ("Robot-o.xls","x","$A$2",TIME)

XLWriteArray ("Robot-o.xls","x","$B$2",R1La)

XLWriteArray ("Robot-o.xls","x","$C$2",R2La)

XLWriteArray ("Robot-o.xls","x","$D$2",R3La)

XLWriteArray ("Robot-o.xls","x","$E$2",R4La)

XLWriteArray ("Robot-o.xls","x","$F$2",R5La)

ENDIF

IF TIME > 1

R1La = R1L

R2La = R2L

R3La = R3L

R4La = R4L

R5La = R5L

tt = TIME + 1

XLWriteArray ("Robot-o.xls","x","$A$" + @tt,TIME)

XLWriteArray ("Robot-o.xls","x","$B$" + @tt,R1L)

XLWriteArray ("Robot-o.xls","x","$C$" + @tt,R2L)

XLWriteArray ("Robot-o.xls","x","$D$" + @tt,R3L)

XLWriteArray ("Robot-o.xls","x","$E$" + @tt,R4L)

XLWriteArray ("Robot-o.xls","x","$F$" + @tt,R5L)

ENDIF

Robot2-Program-Actions: Input Part

IF R1La = 1 AND R2La = 1 AND R3La = 1

X2 = 0

r2t = 1

ELSEIF R1La = 1 AND R2La = 1 AND R3La = 0

X2 = 1

r2t = 2

ELSEIF R1La = 1 AND R2La = 0 AND R3La = 1

X2 = 0

r2t = 3

ELSEIF R1La = 1 AND R2La = 0 AND R3La = 0

X2 = 1

r2t = 4

ELSEIF R1La = 0 AND R2La = 1 AND R3La = 1

X2 = 1

r2t = 5

ELSEIF R1La = 0 AND R2La = 1 AND R3La = 0

X2 = 0

r2t = 6

ELSEIF R1La = 0 AND R2La = 0 AND R3La = 1

X2 = 1

r2t = 7

ELSEIF R1La = 0 AND R2La = 0 AND R3La = 0

X2 = 0

r2t = 8

ENDIF

R2L = X2

timex = TIME

Robot3-Program-Actions: Input Part

IF R2La = 1 AND R3La = 1 AND R4La = 1

X3 = 0

r3t = 1

ELSEIF R2La = 1 AND R3La = 1 AND R4La = 0

X3 = 1

r3t = 2

ELSEIF R2La = 1 AND R3La = 0 AND R4La = 1

X3 = 0

r3t = 3

ELSEIF R2La = 1 AND R3La = 0 AND R4La = 0

X3 = 1

r3t = 4

ELSEIF R2La = 0 AND R3La = 1 AND R4La = 1

X3 = 1

r3t = 5

ELSEIF R2La = 0 AND R3La = 1 AND R4La = 0

X3 = 0

r3t = 6

ELSEIF R2La = 0 AND R3La = 0 AND R4La = 1

X3 = 1

r3t = 7

ELSEIF R2La = 0 AND R3La = 0 AND R4La = 0

X3 = 0

r3t = 8

ENDIF

R3L = X3

Robot4-Program-Actions: Input Part

IF R3La = 1 AND R4La = 1 AND R5La = 1

X4 = 0

r4t = 1

ELSEIF R3La = 1 AND R4La = 1 AND R5La = 0

X4 = 1

r4t = 2

ELSEIF R3La = 1 AND R4La = 0 AND R5La = 1

X4 = 0

r4t = 3

ELSEIF R3La = 1 AND R4La = 0 AND R5La = 0

X4 = 1

r4t = 4

ELSEIF R3La = 0 AND R4La = 1 AND R5La = 1

X4 = 1

r4t = 5

ELSEIF R3La = 0 AND R4La = 1 AND R5La = 0

X4 = 0

r4t = 6

ELSEIF R3La = 0 AND R4La = 0 AND R5La = 1

X4 = 1

r4t = 7

ELSEIF R3La = 0 AND R4La = 0 AND R5La = 0

X4 = 0

r4t = 8

ENDIF

R4L = X4

Robot5-Program-Actions: Input Part

IF R4La = 1 AND R5La = 1 AND R1La = 1

X5 = 0

r5t = 1

ELSEIF R4La = 1 AND R5La = 1 AND R1La = 0

X5 = 1

r5t = 2

ELSEIF R4La = 1 AND R5La = 0 AND R1La = 1

X5 = 0

r5t = 3

ELSEIF R4La = 1 AND R5La = 0 AND R1La = 0

X5 = 1

r5t = 4

ELSEIF R4La = 0 AND R5La = 1 AND R1La = 1

X5 = 1

r5t = 5

ELSEIF R4La = 0 AND R5La = 1 AND R1La = 0

X5 = 0

r5t = 6

ELSEIF R4La = 0 AND R5La = 0 AND R1La = 1

X5 = 1

r5t = 7

ELSEIF R4La = 0 AND R5La = 0 AND R1La = 0

X5 = 0

r5t = 8

ENDIF

R5L = X5

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